Flow Rate Formula (original) (raw)
Last Updated : 4 Feb, 2024
Flow rate is the measurement of how much liquid travels in a given length of time, as the name implies. Its current is also affected by the pipe's diameter. The flow rate of a fluid is its ability to flow from one point to another.
What is Flow Rate?
The flow rate of a liquid is defined as the measure of the volume of liquid that moves in a certain amount of time. It is the amount of fluid that moves through a given area in a given amount of time. It can be interpreted as the velocity of the liquid for a cross-sectional area of the pipe.
It varies directly with the area of the pipe and the velocity with which the liquid flows in a pipe.
- It is denoted by the symbol Q.
- Its standard unit of measurement is cubic meters per second (m3/s) and the dimensional formula is given by [M0L3T-1].
**Flow Rate Formula
The formula for flaw rate is given as,
**Q = Av
where,
- Q is the flow rate,
- A is area of cross section of pipe,
- v is the velocity of the fluid.
The Flow rate Q can also be defined to be the volume of fluid passing by some position through an area during a period of time.
**Q = V / t
where,
- V is the volume of fluid and
- t is the period of time taken.
**Sample Problems
**Problem 1: Calculate the flow rate of liquid moving in a pipe of cross-section 20 m 2 at a velocity of 10 m/s.
**Solution:
We have,
A = 20
v = 10
Using the formula we have,
Q = Av
= 20 (10)
= 200 m 3 /s
**Problem 2: Calculate the flow rate of liquid moving in a pipe of cross-section 15 m 2 at a velocity of 12 m/s.
**Solution:
We have,
A = 15
v = 12
Using the formula we have,
Q = Av
= 15 (12)
= 180 m 3 /s
**Problem 3: Calculate the flow rate of a liquid moving in a pipe of radius 2 m at a velocity of 10 m/s.
**Solution:
We have,
r = 2
v = 10
Calculate the cross section area.
A = πr2
= 3.14 (2) (2)
= 12.56 m2
Using the formula we have,
Q = Av
= 12.56 (10)
= 125.6 m 3 /s
**Problem 4: Calculate the velocity of the liquid if its flow rate is 100 m 3 /s in a pipe of cross-section 50 m 2 .
**Solution:
We have,
Q = 100
A = 50
Using the formula we have,
Q = Av
or
v = Q/A
= 100/50
= **2 m/s
**Problem 5: Calculate the velocity of the liquid if its flow rate is 144 m 3 /s in a pipe of cross-section 36 m 2 .
**Solution:
We have,
Q = 144
A = 36
Using the formula we have,
Q = Av
or
v = Q/A
= 144/36
= 4 m/s
**Problem 6: Calculate the area of the cross-section if its flow rate is 90 m 3 /s moving at a velocity of 15 m/s.
**Solution:
We have,
Q = 90
v = 15
Using the formula we have,
Q = Av
or A = Q/v
= 90/15
= 6 m 2
**Problem 7: Calculate the area of the cross-section if its flow rate is 120 m 3 /s moving at a velocity of 45 m/s.
**Solution:
We have,
Q = 120
v = 45
Using the formula we have,
Q = Av
or
A = Q/v
= 120/45
= **2.66 m 2